Literature Cited
I. Ozsvath and E. Schucking, “An anti-Mach metric,” Recent Developments in General Relativity, Pergamon Press-PMN (1962), pp. 339–350.
A. V. Levichev, “Methods of investigation of the causal structure of homogeneous Lorentz manifolds,” Sib. Mat. Zh.,31, No. 3, 39–54 (1990).
A. V. Levichev, “The causal structure of a Lorentzian manifold determines its conformal geometry,” Dokl. Akad. Nauk SSSR,293, No. 6, 1301–1305 (1987).
D. B. Malament, “The class of continuous timelike curves determines the topology of space-time,” J. Math. Phys.,18, No. 7, 1399–1404 (1977).
S. P. Gavrilov, “Left-invariant metrics on simply connected Lee groups containing an abelian subgroup of codimension 1,” Gravitation and the Theory of Relativity Vol. 21, Kazan' (1984), pp. 13–47.
V. A. Kushmantseva and A. V. Levichev, “Left-invariant Lorentz metrics on a four-dimensional Lee group,” Sib. Mat. Zh., Moscow (1986), Depoosited in VINITI, 08.04.86, No. 2506-B86.
J. Beem and P. Ehrlich, Global Lorentzian Geometry, Marcel Dekker, New York (1981).
S. P. Gavrilov, “Geodesics of left-invariant metrics on a connected two-dimensional nonabelian Lee group,” Gravitation and the Theory of Relativity, Vol. 18, Kazan' (1981), pp. 28–44.
A. V. Levichev, “On sufficient conditions for violation of chronology in a homogeneous Lorentz space,” in: Proceedings of the All-Union Conference on Global Geometry, Novosibirsk (1987), Inst. Mat. Sib. Otd. Akad. Nauk SSSR (1987), p. 69.
V. I. Arnol'd, Mathematical Methods of Classical Mechanics [in Russian], Nauka, Moscow (1974).
Additional information
Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 6, pp. 90–95, November–December, 1990.
Rights and permissions
About this article
Cite this article
Kushmantseva, V.A., Levichev, A.V. The causal structure of an anti-Mach metric. Sib Math J 31, 950–955 (1990). https://doi.org/10.1007/BF00970060
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00970060